Description: Surrogates Early Warning Signals

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Description

surrogates_ews is used to estimate distributions
of trends in statistical moments from different surrogate
timeseries generated after fitting an ARMA(p,q) model on
the data. The trends are estimated by the nonparametric
Kendall tau correlation coefficient and can be compared
to the trends estimated in the original timeseries to
produce probabilities of false positives.

Arguments

timeseries

a numeric vector of the observed
univariate timeseries values or a numeric matrix where
the first column represents the time index and the second
the observed timeseries values. Use vectors/matrices with
headings.

indicator

is the statistic (leading indicator)
selected for which the surrogate timeseries are produced.
Currently, the indicators supported are: ar1
autoregressive coefficient of a first order AR model,
sd standard deviation, acf1 autocorrelation
at first lag, sk skewness, kurt kurtosis,
cv coeffcient of variation, returnrate, and
densratio density ratio of the power spectrum at
low frequencies over high frequencies.

winsize

is the size of the rolling window
expressed as percentage of the timeseries length (must be
numeric between 0 and 100). Default valuise 50%.

detrending

the timeseries can be
detrended/filtered prior to analysis. There are three
options: gaussian filtering, linear
detrending and first-differencing. Default is
no detrending.

bandwidth

is the bandwidth used for the Gaussian
kernel when gaussian filtering is selected. It is
expressed as percentage of the timeseries length (must be
numeric between 0 and 100). Alternatively it can be given
by the bandwidth selector bw.nrd0
(Default).

boots

the number of surrogate data. Default is
100.

logtransform

logical. If TRUE data are
logtransformed prior to analysis as log(X+1). Default is
FALSE.

interpolate

logical. If TRUE linear interpolation
is applied to produce a timeseries of equal length as the
original. Default is FALSE (assumes there are no gaps in
the timeseries).

Details

see ref below

Value

surrogates_ews returns a matrix that contains:

Kendall tau estimate original

the trends of the
original timeseries.

Kendall tau p-value original

the p-values of the
trends of the original timeseries.

Kendall tau estimate surrogates

the trends of the
surrogate timeseries.

Kendall tau p-value surrogates

the associated
p-values of the trends of the surrogate timeseries.

significance p

the p-value for the original
Kendall tau rank correlation estimate compared to the
surrogates.

In addition, surrogates_ews returns a plot with
the distribution of the surrogate Kendall tau estimates
and the Kendall tau estimate of the original series.
Vertical lines indicate the 5% and 95% significance
levels.

Author(s)

References

Dakos, V., et al (2008). "Slowing down as an early
warning signal for abrupt climate change."
Proceedings of the National Academy of Sciences
105(38): 14308-14312

Dakos, V., et al (2012)."Methods for Detecting Early
Warnings of Critical Transitions in Time Series
Illustrated Using Simulated Ecological Data." PLoS
ONE 7(7): e41010. doi:10.1371/journal.pone.0041010